package com.shawn.datastructure.graph;

import java.lang.*;

/**
 * A Java program for Prim's Minimum Spanning Tree (MST) algorithm. adjacency matrix representation
 * of the graph
 */
class PrimMST {

	// Number of vertices in the graph
	private static final int V = 5;

	// A utility function to find the vertex with minimum key
	// value, from the set of vertices not yet included in MST
	int minKey(int key[], Boolean mstSet[]) {
		// Initialize min value
		int min = Integer.MAX_VALUE, min_index = -1;

		for (int v = 0; v < V; v++) {
			if (mstSet[v] == false && key[v] < min) {
				min = key[v];
				min_index = v;
			}
		}

		return min_index;
	}

	// A utility function to print the constructed MST stored in
	// parent[]
	void printMST(int parent[], int n, int graph[][]) {
		System.out.println("Edge   Weight");
		for (int i = 1; i < V; i++) {
			System.out.println(parent[i] + " - " + i + "    " +
				graph[i][parent[i]]);
		}
	}

	// Function to construct and print MST for a graph represented
	//  using adjacency matrix representation
	void primMST(int graph[][]) {
		// Array to store constructed MST
		int parent[] = new int[V];

		// Key values used to pick minimum weight edge in cut
		int key[] = new int[V];

		// To represent set of vertices not yet included in MST
		Boolean mstSet[] = new Boolean[V];

		// Initialize all keys as INFINITE
		for (int i = 0; i < V; i++) {
			key[i] = Integer.MAX_VALUE;
			mstSet[i] = false;
		}

		// Always include first 1st vertex in MST.
		key[0] = 0;     // Make key 0 so that this vertex is
		// picked as first vertex
		parent[0] = -1; // First node is always root of MST

		// The MST will have V vertices
		for (int count = 0; count < V - 1; count++) {
			// Pick thd minimum key vertex from the set of vertices
			// not yet included in MST
			int u = minKey(key, mstSet);

			// Add the picked vertex to the MST Set
			mstSet[u] = true;

			// Update key value and parent index of the adjacent
			// vertices of the picked vertex. Consider only those
			// vertices which are not yet included in MST
			for (int v = 0; v < V; v++)

			// graph[u][v] is non zero only for adjacent vertices of m
			// mstSet[v] is false for vertices not yet included in MST
			// Update the key only if graph[u][v] is smaller than key[v]
			{
				if (graph[u][v] != 0 && mstSet[v] == false &&
					graph[u][v] < key[v]) {
					parent[v] = u;
					key[v] = graph[u][v];
				}
			}
		}

		// print the constructed MST
		printMST(parent, V, graph);
	}

	public static void main(String[] args) {
        /* Let us create the following graph
           2    3
        (0)--(1)--(2)
        |    / \   |
        6| 8/   \5 |7
        | /      \ |
        (3)-------(4)
             9          */
		PrimMST t = new PrimMST();
		int graph[][] = new int[][]{{0, 2, 0, 6, 0},
			{2, 0, 3, 8, 5},
			{0, 3, 0, 0, 7},
			{6, 8, 0, 0, 9},
			{0, 5, 7, 9, 0},
		};

		// Print the solution
		t.primMST(graph);
	}
}
